New to Java

I searched the tutorials and the Javadoc but couldn't find how to force a read-only JTextArea in a JScrollPane to keep scrolling to the end of the display when I append text.

At the moment the vertical scroll bar sits at the beginning, while appended text just disappears out of sight.

This is my code:

            progressText = new JTextArea(10, 20);
            progressText.setEditable(false);
            progressScroll = new JScrollPane(progressText, JScrollPane.VERTICAL_SCROLLBAR_AS_NEEDED,
                    JScrollPane.HORIZONTAL_SCROLLBAR_AS_NEEDED);

There must be a simple solution to this, but I can't find it!

I suspect I need to implement a DocumentListener, but don't know what to put in it.